Optical parametric circuit and optical circuit using the same

ABSTRACT

The present invention provides an optical parametric circuit for separating four-wave-mixing wave(s) (FWM wave(s)) from signal wave(s) and/or pump waves without using a wavelength filtering device, and optical circuits using the same. The optical parametric circuit of the present invention is made by connecting two output ports of a 2×2 optical directional coupler to a nonlinear optical medium via dispersive optical media, each of which has a specific length and a specific propagation constant. By inputting signal waves having carrier angular frequencies ω Sj  (j=1, 2, . . . N) and pump waves having carrier angular frequencies ω P1 , ω P2  into the first input port of the optical directional coupler, the FWM waves, generated in the nonlinear optical medium, having carrier angular frequencies ω fj  (=ω P1  +ω P2  -ω S ) are output from the second input port of the optical directional coupler. By inputting the signal waves and the pump waves from different input ports of the directional coupler, it is possible to separate amplified signal waves and the FWM waves from the pump waves. By adjusting the lengths and the propagation constants of the dispersive optical media, the amplified signal waves are separated from the pump waves and the FWM wave. The optical parametric circuit is used for wavelength conversion of optical signals, parametric amplification of optical signals, optical phase conjugation (spectral inversion) and for all-optical switching and for optical circuits using the same, for example, optical logic circuits, optical time-division multi/demultiplexers and/or optical sampling circuits.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an optical parametric circuit used forwavelength conversion of optical signals, parametric amplification ofoptical signals, optical phase conjugation (spectral inversion) and forall-optical switching by utilizing the third-order optical parametriceffect induced in a nonlinear optical medium, and to optical circuitsusing the same, for example, optical logic circuits, opticaltime-division multi/demultiplexers and/or optical sampling circuits.

2. Description of the Related Art

FIG. 53 shows a configuration of a conventional optical parametriccircuit.

This figure illustrates a process of generating the third-order opticalparametric effect by coupling a signal wave S (of carrier angularfrequency ω_(s)) shown in FIG. 54A with pump waves P₁, P₂ (of carrierangular frequencies ω_(P1), ω_(P2)) shown in FIG. 54B into an opticalwavelength-division multiplexer 11 (refer to FIG. 54C) followed by asimultaneous inputting into a nonlinear optical medium 12 andpropagating therefrom to induce the third-order optical parametriceffect. The signal wave S is thus amplified (which is denoted by S'),and, through a four-wave mixing process, four-wave- mixing (shortened toFWM hereinbelow) wave F having a carrier angular frequency ω_(f) isgenerated (refer to FIG. 54D).

Here, the carrier angular frequencies ω_(S), ω_(P1), ω_(P2), ω_(f) ofthe signal wave S, pump waves P₁, P₂ and FWM wave F, are governed by thelaw of conservation of energy as expressed in the following equation:

    ω.sub.S +ω.sub.f =ω.sub.P1 +ω.sub.P2

The FWM wave F has a mirror symmetry with the spectrum of signal wave Swith respect of the carrier angular frequency (ω_(P1) +ω_(P2))/2, andfunctions also as the optical phase conjugation wave for the signal waveS. In other words, this optical parametric circuit can function as aphase conjugation wave generation circuit. FIG. 55 shows a circuitconfiguration using a degenerate pump wave P (carrier angular frequencyω_(P)) and FIGS. 56A to 56D show the spectra of the optical wavescorresponding to the spectra shown in FIGS. 54A to 54D. In the drawings,the signal wave S and FWM wave F are shown as right-angle triangularmirror images, for illustrative purposes, to indicate the fact that theFWM wave F is the phase conjugate wave of the signal wave S.

Such an optical parametric circuit can also serve as a wavelengthconversion circuit to perform simultaneous wavelength conversion of eachwavelength of wavelength-division multiplexed signals. For example, uponinjection of an N number of signal waves S₁ ˜S_(N) (carrier angularfrequency ω_(S1) ˜ω_(SN)), FWM waves ωF₁ ˜F_(N) are generated (carrierangular frequency ω_(f1) ˜ω_(fN) where ω_(fj) =ω_(P1) +ω_(P2) -ω_(Sj)for j=1˜N) thus providing simultaneous wavelength conversion of eachwave of the wavelength-division multiplexed signals. FIG. 57 shows acircuit configuration based on a degenerate pump wave P (carrier angularfrequency ω_(P)). FIGS. 58A to 58D show the spectra corresponding to thespectra shown in FIGS. 56A to 56D. In these figures, filled and unfilledtriangles are used for showing the correspondence between signal wavesS₁ ˜S_(N) and FWM waves F₁ ˜F_(N).

An example of application of the parametric circuit as an opticalamplification circuit is shown in FIG. 59. Propagation patterns of eachwave to the output port of the nonlinear optical medium 12 are the sameas those presented in FIGS. 54A˜54D. The amplified signal S' is shown inFIG. 54D.

Using the configuration shown in FIGS. 53, 55 and 57, signal wave S (S₁˜S_(N)), pump waves (P₁, P₂ and P) and FWM waves (F₁ ˜F_(N)) are alloutput colinearly from the nonlinear optical medium 12, therefore, toobtain only the FWM waves F (F₁ ˜F_(N)), it is necessary to employ awavelength filter 13 which passes only those waves having carrierangular frequencies ω_(f) (ω_(f1) ˜ω_(fN)). The output spectra from thewavelength filter 13 are shown in FIGS. 54E, 56E and 58E. By using theconfiguration as an optical amplification circuit of FIG. 59, it isnecessary to use a wavelength filter 29 which passes only the amplifiedsignal wave S' of carrier angular frequency ω_(S). The output spectrumfrom the wavelength filter 29 is shown in FIG. 60.

When the optical parametric circuit is to be used as an FWM wavegenerator, it is necessary to pack the carrier angular frequenciesω_(S), ω_(P1) and ω_(P2) to increase the conversion gain (expressed asFWM wave intensity/signal wave intensity) of signal wave S to FWM waveF, as well as increase the pump wave intensity. Similarly, when theoptical parametric circuit is to be used as an optical parametricamplifier, it is necessary to pack the carrier angular frequencies,ω_(S), ω_(P1), ω_(P2), and increase the pump wave intensity to increasethe amplification gain of the signal wave.

Therefore, it is necessary for the wavelength filter 13 to possess acapability to suppress the pump wave intensity, which is higher relativeto the FWM wave intensity, but pass the FWM waves having carrier angularfrequencies which are closely packed with respect to the pump waves.However, it is difficult to sufficiently suppress the pump wave usingonly one wavelength filter, and therefore, it is general practice toemploy a multi-stage optical filter. Therefore, the FWM wave or thesignal wave suffers loss of the power and limitation of the bandwidth,and the circuit arrangement has been complicated. In the case of usingthe optical parametric circuit as the optical amplification circuit,there have been similar problems.

Also, in the conventional optical parametric circuits, when a phaseconjugate signal (i.e. FWM wave F) is generated upon injection of ansignal wave S, the carrier angular frequency is shifted from ω_(S) toω_(f) (=ω_(P1) +ω_(P2) -ω_(S)), using the examples of FIGS. 56A and 56E.This presents a problem that when using the optical parametric circuitas a phase conjugation circuit in an optical fiber transmission system,the carrier angular frequency of transmitted optical signals is changedby passing through the phase conjugation circuit.

Furthermore, when the optical parametric circuit is to be used as asimultaneous wavelength conversion circuit for wavelength-divisionmultiplexed signals, if the carrier angular frequencies ω_(Sm), ω_(Sn)of the two signal waves S_(m), S_(n) and the carrier angular frequenciesω_(P1), ω_(P2) of the pump waves are related in such a way to satisfythe equation:

    ω.sub.Sm +ω.sub.Sn =ω.sub.P1 +ω.sub.P2

then the carrier angular frequencies of the FWM waves F_(m) and F_(n)are set to ω_(Sn) and ω_(Sm), meaning that the effect of interchangingthe carrier angular frequencies of the signal waves would be obtained.However, in the conventional optical parametric circuits, the carrierangular frequencies of the FWM wave F_(m) becomes equal to that of thesignal wave S_(n), and similarly, the carrier angular frequencies of theFWM wave F_(n) becomes equal to that of the signal wave S_(m).Therefore, it is not possible to separate the FWM waves F_(m) and F_(n)from the signal waves S_(n) and S_(m) using any wavelength filteringdevices.

SUMMARY OF THE INVENTION

It is an object of the present invention to provide an opticalparametric circuit to enable separation of four-wave-mixing wave(s) fromsignal wave(s) and pump waves without using wavelength filtering means,or to enable a separation of a four-wave-mixing wave from either signalwave(s) or pump waves, and to apply this optical circuit to functionaldevices.

The first object to separate generated four-wave-mixing wave(s) fromsignal wave(s) and pump waves is achieved in an optical parametriccircuit comprising: a nonlinear optical medium for generating waveshaving carrier angular frequencies ω_(fj) (=ω_(P1) +ω_(P2) -ω_(Sj) ;j=1, 2, . . . N) from waves having carrier angular frequencies ω_(Sj),ω_(P1), and ω_(P2) ; an optical directional coupler having a first inputport, second input port, first output port and second output port forseparating waves having carrier angular frequencies ω_(Sj), ω_(P1),ω_(P2) and ω_(fj) into respective waves of an equal intensity and apolarization state; a first dispersive optical medium having a lengthdimension L₁ and a propagation constant K₁ (ω) for connecting the firstoutput port of the optical directional coupler with one end of thenonlinear optical medium; a second dispersive optical medium having alength dimension L₂ and a propagation constant K₂ (ω) for connecting thesecond output port of the optical directional coupler with the other endof the nonlinear optical medium; wherein signal waves having carrierangular frequencies ω_(S1), ω_(S2), . . . , ω_(SN) and pump waves havingcarrier angular frequencies ω_(P1), ω_(P2) are injected into the firstinput port of the optical directional coupler so as to outputfour-wave-mixing waves ω_(fj) generated in the nonlinear optical mediumfrom the second input port of the optical directional coupler, andwherein the carrier angular frequencies ω_(Sj), ω_(P1), ω_(P2) andω_(fj) are related by an expression:

    {K.sub.2 (ω.sub.fj)+K.sub.2 (ω.sub.Sj)-K.sub.2 (ω.sub.P1)-K.sub.2 (ω.sub.P2)}L.sub.2 ={K.sub.1 (ω.sub.fj)+K.sub.1 (ω.sub.Sj)-K.sub.1 (ω.sub.P1)-K.sub.1 (ω.sub.P2)}L.sub.1 +(2n-1±α)π

where n is an integer and an allowable error α is in a range 0≦α< 1/2.

The optical parametric circuit configuration presented above enables theseparation of the generated four-wave-mixing waves (FWM waves) from thesignal waves and the pump waves, without using wavelengh-divisionoptical demultiplexing means such as wavelength filters, by using thedispersive optical media which satisfy the specified conditions.

Accordingly, bandwidth limitations imposed by wavelength filters do notapply, and ultrafast processing of optical signals becomes possible andclose packing of the carrier angular frequencies of the signal and pumpwaves enables to improve the generation efficiency of FWM waves.

The optical parametric circuit of the present invention also enables aheretofore unachieved task of separating optical phase conjugationwaves, having carrier angular frequencies equal to or near the carrierangular frequencies of the signal waves, from the signal and pump waves.

The parametric circuit of the present invention also enables aheretofore unachieved task of wavelength interchange ofwavelength-division multiplexed signal waves.

Even if optical noise components are included in the signal waves andpump waves, they are eliminated together with the signal and pump waves,thus improving the signal to noise ratio of FWM waves (phase conjugatewaves and wavelength converted waves) by eliminating superposition ofthe noise signal components thereon.

Also, the second object to separate FWM wave(s) from either pump wavesor signal wave(s) is achieved by using the same configuration as theabove optical parametric circuit wherein the pump waves are injectedinto the first input port of the optical directional coupler, while thesignal waves are injected into the second input port.

If the carrier angular frequencies ω_(Sj), ω_(P1), ω_(P2), and ω_(fj)are related by an expression:

    {K.sub.2 (ω.sub.fj)+K.sub.2 (ω.sub.Sj)-K.sub.2 (ω.sub.P1)-K.sub.2 (ω.sub.P2)}L.sub.2 ={K.sub.1 (ω.sub.fj)+K.sub.1 (ω.sub.Sj)-K.sub.1 (ω.sub.P1)-K.sub.1 (ω.sub.P2)}L.sub.1 +(2n±α)π

the FWM waves generated in the nonlinear optical medium are output withthe signal waves amplified in the nonlinear optical medium from thesecond input port, and separated from the pump waves which are outputfrom the first input port.

On the other hand, if the carrier angular frequencies ω_(Sj), ω_(P1),ω_(P2), and ω_(fj) are related by an expression:

    {K.sub.2 (ω.sub.fj)+K.sub.2 (ω.sub.Sj)-K.sub.2 (ω.sub.P1)-K.sub.2 (ω.sub.P2)}L.sub.2 ={K.sub.1 (ω.sub.fj)+K.sub.1 (ω.sub.Sj)-K.sub.1 (ω.sub.P1)-K.sub.1 (ω.sub.P2)}L.sub.1 +(2n-1 ±α)π

the FWM waves generated in the nonlinear optical medium are output withthe pump waves from the first input port, and separated from the signalwaves amplified in the nonlinear optical medium which are output fromthe second input port.

In the above cases, by using appropriate optical dispersive media, it ispossible to couple the signal wave(s) and the pump waves and to separatethe generated FWM wave(s) from either the pump waves or the signalwave(s) using the optical demultiplexing means such as wavelengthfilters. Even if optical noise components are contained in the pumpwaves input, the optical noise components are not output with either thegenerated FWM waves or the amplified signal waves.

It should be noted that signal waves of carrier angular frequenciesω_(Sj) (j=1, 2, . . . N) include a single frequency signal wave having asingular frequency ω_(S1) or ω_(S), and, of course, in this case, theoutput FWM wave having a singular frequency ω_(f) (=ω_(P1) +ω_(P2)-ω_(S)) is output. Furthermore, either of the lengths L₁ and L₂ of thefirst and second dispersive optical media used in the parametric circuitof the present invention may be zero, i.e. the present inventionincludes those cases in which only one dispersive optical medium isused.

An FWM circuit using the so-called Sagnac interference device butwithout using the dispersive optical media is known in "A fiberfrequency shifter with broad bandwidth, high conversion efficiency, pumpand pump ASE cancellation, and rapid tunability for WDM opticalnetworks", IEEE Photonics Technology Letters, Eric A. Swanson and JohnD. Moores, vol. 6, pp260-263, (1994). In this FWM circuit, the pumpwaves and the signal wave are injected into the different input ports ofan optical directional coupler, and the generated FWM wave is outputwith the signal wave. Therefore, when the signal waves and the FWM waveshave the same or similar carrier angular frequencies, it is not possibleto isolate the FWM waves. This FWM circuit is therefore inapplicable toapplications such as spectral inversion circuit with no wavelength shiftor wavelength interchanging circuit of WDM signal waves.

As explained above, by using the optical parametric circuit of thepresent invention, it is possible to perform high efficiency, high S/Nratio, and wide-bandwidth optical processing such as wavelengthconversion, phase conjugation generation (spectral inversion), opticalsignal amplification and all-optical switching, without the influence ofhigh-power pump waves. All-optical switching includes such applicationsas optical pulse multiplexing circuit, optical pulse demultiplexingcircuit, and optical waveform sampling circuit.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic drawing of the configuration of a Embodiment 1 ofthe optical parametric circuit of the present invention.

FIGS. 2A˜2C present the spectra of each wave in Embodiment 1.

FIGS. 3A˜3C present the spectra of each wave in Variation 1 ofEmbodiment 1.

FIG. 4 is a configuration of the optical parametric circuit in Variation2 of Embodiment 1.

FIGS. 5A and 5B present the spectra of each wave in Variation 2 ofEmbodiment 1.

FIG. 6 is a configuration of the optical parametric circuit in Variation3 of Embodiment 1.

FIGS. 7A˜7C present the spectra of each wave in Variation 3 ofEmbodiment 1.

FIGS. 8A and 8B present spectra of each wave in a Variation 4 ofEmbodiment 1 to facilitate separation of four-wave-mixing wave.

FIG. 9 is a configuration of the optical parametric circuit in Variation5 of Embodiment 1.

FIGS. 10A and 10B present the spectra of each wave in Variation 5 ofEmbodiment 1.

FIG. 11 is a schematic drawing of the configuration of Embodiment 2 ofthe optical parametric circuit of the present invention.

FIG. 12 is a configuration of the optical parametric circuit inVariation 1 of Embodiment 2.

FIG. 13 is a schematic drawing of the configuration of Embodiment 3 ofthe optical parametric circuit of the present invention.

FIGS. 14A and 14B present the spectra of each wave in Embodiment 3.

FIG. 15 is a schematic drawing of the configuration of Embodiment 4 ofthe optical parametric circuit of the present invention.

FIG. 16 is a schematic drawing of the configuration of Embodiment 5 ofthe optical parametric circuit of the present invention.

FIGS. 17A and 17B illustrate the time-resolved spectra of each wave inEmbodiment 6 of the present invention.

FIGS. 18A and 18B illustrate the time-resolved spectra of each wave inEmbodiment 6 of the present invention.

FIG. 19 illustrates the time-resolved spectra of each wave in Embodiment7 of the present invention.

FIG. 20 illustrates the time-resolved spectra of each wave in Embodiment7 of the present invention.

FIG. 21 illustrates the time-resolved spectra of each wave, which wasobtained by a practical operation example of the optical phaseconjugation circuit of the present invention.

FIG. 22 is a schematic drawing of the configuration of Embodiment 8 ofthe optical parametric circuit of the present invention.

FIGS. 23A˜23D show optical waveforms corresponding to each carrierfrequency in Embodiment 8.

FIG. 24 presents a schematic drawing of the configuration of Variation 1of Embodiment 8 of the optical parametric circuit of the presentinvention.

FIGS. 25A˜25D show optical waveforms corresponding to each carrierfrequency in Variation 1 of Embodiment 8.

FIG. 26 is a schematic drawing of the configuration of Embodiment 9 ofthe optical parametric circuit of the present invention.

FIGS. 27A˜27E show optical waveforms corresponding to each carrierfrequency in Embodiment 9.

FIG. 28 is a schematic drawing of the configuration of Embodiment 10 ofthe optical parametric circuit of the present invention.

FIGS. 29A˜29D show optical waveforms corresponding to carrier frequencyin Embodiment 10.

FIGS. 30A and 30B are schematic drawings of the configurations ofEmbodiment 11 of the optical parametric circuit of the presentinvention.

FIGS. 31A˜31G present the spectra of each wave in Embodiment 11.

FIG. 32 presents a schematic drawing of the configuration of Variation 1of Embodiment 11 of the optical parametric circuit of the presentinvention.

FIGS. 33A˜33C present the spectra of each wave in Variation 1 ofEmbodiment 11.

FIG. 34 is a schematic drawing of the configuration of Embodiment 12 ofthe optical parametric circuit of the present invention.

FIG. 35 is a schematic drawing of the configuration of Embodiment 13 ofthe optical parametric circuit of the present invention.

FIG. 36 is a schematic drawing of the configuration of Embodiment 14A ofthe optical parametric circuit of the present invention.

FIG. 37 shows the spectrum of an amplified output signal.

FIG. 38 is a schematic drawing of the configuration of Embodiment 14B ofthe optical parametric circuit of the present invention.

FIG. 39 shows the spectra of a pump wave and an FWM wave both of whichare output from port 20a.

FIGS. 40A and 40B are schematic drawings of the configuration ofEmbodiment 15 of the optical parametric circuit of the presentinvention.

FIG. 41 shows the spectrum of an FWM wave output through a wavelengthfilter 13.

FIG. 42 is a schematic drawing of the configuration of an opticalparametric circuit in Embodiment 16 of the present invention.

FIGS. 43A˜43E show the optical waveforms corresponding to each carrierfrequency in Embodiment 16.

FIG. 44 is a schematic drawing of the optical parametric circuit inVariation 1 of Embodiment 16 of the present invention.

FIGS. 45A˜45F show the optical waveforms corresponding to each carrierfrequency in Variation 1 of Embodiment 16.

FIG. 46 is a schematic drawing of the optical parametric circuit inVariation 2 of Embodiment 16 of the present invention.

FIGS. 47A and 47B show the optical waveforms corresponding to eachcarrier frequency in Variation 2 of Embodiment 16.

FIG. 48 is a schematic drawing of the configuration of an opticalparametric circuit in Embodiment 17 of the present invention.

FIGS. 49A˜49F show the optical waveforms corresponding to each carrierfrequency in Embodiment 17.

FIG. 50 is a schematic drawing of the configuration of an opticalparametric (waveform sampling) circuit in Embodiment 18 of the presentinvention.

FIG. 51 is similarly a schematic drawing of the configuration of anoptical parametric (waveform sampling) circuit in Embodiment 18 of thepresent invention.

FIGS. 52A˜52D show each wave in the optical parametric (waveformsampling) circuit in Embodiment 18.

FIG. 53 is a schematic diagram of a conventional optical parametriccircuit.

FIGS. 54A˜54E show the spectra of each wave in the circuit shown in FIG.53.

FIG. 55 is a schematic diagram of a conventional optical phaseconjugation circuit.

FIGS. 56A˜56E show the spectra of each wave in the circuit shown in FIG.55.

FIG. 57 is a schematic diagram of a conventional simultaneous wavelengthconversion circuit for wavelength-division multiplexed signal waves.

FIGS. 58A˜58E show the spectra of each wave in the circuit shown in FIG.57.

FIG. 59 is a schematic diagram of a conventional optical parametricamplifier circuit.

FIG. 60 shows the spectrum of the signal wave in the circuit shown inFIG. 59.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Preferred embodiments will be explained with reference to the drawings.

Embodiment 1

FIG. 1 is a schematic diagram of the optical parametric circuit of thepresent invention being used as an FWM wave generation circuit.

With reference to FIG. 1, a nonlinear optical medium 12 is insertedbetween two dispersive optical media 21, 22 to which ports 20c, 20d of a2×2 optical directional coupler 20 are respectively connected. Theoptical directional coupler 20 has a capability to separate opticalwaves having carrier frequencies (shortened to carrier frequencyhereinbelow) ω_(S), ω_(P1), ω_(P2), ω_(f) (=ω_(P1) +ω_(P2) -ω_(S)) atequal intensities and equal polarization state. The length of thedispersive optical medium 21 which joins pore 20c with the nonlinearoptical medium 12 is denoted by L₁ and the propagation constant thereinby K₁ (ω), and the length of the dispersive optical medium 22 whichjoins port 20d and the nonlinear optical medium 12 is denoted by L₂ andthe propagation constant therein by K₂ (ω). A typical example of thedispersive optical medium would be an optical waveguide.

A signal wave S having the carrier frequency ω_(S) and the pump wavesP₁, P₂ having the carrier frequencies ω_(P1), ω_(P2) (refer to FIG. 2A)are injected into the port 20a of the optical directional coupler 20,and are separated at ports 20c, 20d into waves of equal intensities andpolarization states, respectively. However, the phases of the signalwave S_(L) and the pump waves P_(1L), P_(2L) output from port 20d, whichis the cross-port with respect to port 20a, are retarded by 90 degreesfrom the phases of the signal wave S_(R) and the pump waves P_(1R),P_(2R) output from port 20c, which is the through-port with respect toport 20a. Therefore, if the complex electrical field amplitude(hereinafter shortened to complex amplitude) of the signal wave S_(R) atport 20c is denoted by A_(S), and the complex amplitudes of the pumpwaves P_(1R), P_(2R) at port 20c are denoted by A_(P1), A_(P2), then thecomplex amplitude of the signal wave S_(L) at port 20d is given by:A_(S) ·exp(-iπ/2), and the complex amplitudes of the pump waves P_(1L),P_(2L) are given by A_(P1) ·exp(-iπ/2), A_(P2) ·exp(-iπ/2),respectively.

Reviewing the above, the signal wave S_(R) and the pump waves P_(1R),P_(2R) separated to port 20c of the optical directional coupler 20propagates in the direction of the dispersive optical medium21→nonlinear optical medium 12→dispersive optical medium 22→port 20d,i.e. in the clockwise direction. Here, the complex amplitudes A_(SR),A_(P1R), and A_(P2R) of the clockwise signal S_(R) and the pump wavesP_(1R), P_(2R) which are input from port 20c via dispersive opticalmedium 21 into nonlinear optical medium 12 are expressed as follows.

    A.sub.SR =A.sub.S ·exp (-iK.sub.1 (ω.sub.S)L.sub.1)(1)

    A.sub.P1R =A.sub.P1 ·exp (-iK.sub.1 (ω.sub.P1)L.sub.1)(2)

    A.sub.P2R =A.sub.P2 ·exp (-iK.sub.1 (ω.sub.P2)L.sub.1)(3)

In the meanwhile, the signal wave S_(L) and the pump waves P_(1L),P_(2L) separated to port 20d of the optical directional coupler 20propagate in the direction of the dispersive optical medium 22→nonlinearoptical medium 12→dispersive optical medium 21→port 20c, i.e. in thecounter-clockwise direction. Here, the complex amplitudes A_(SL),A_(P1L) and A_(P2L) of the counter-clockwise signal S_(L) and the pumpwaves P_(1L), P_(2L) which are input from port 20d via dispersiveoptical medium 22 into nonlinear optical medium 12 are expressed asfollows.

    A.sub.SL =A.sub.S ·exp (-iK.sub.2 (ω.sub.S)L.sub.2 -iπ/2)(4)

    A.sub.P1L =A.sub.P1 ·exp (-iK.sub.2 (ω.sub.P1)L.sub.2 -iπ/2)                                                 (5)

    A.sub.P2L =A.sub.P2 ·exp (-iK.sub.2 (ω.sub.P2)L.sub.2 -iπ/2)                                                 (6)

Within the nonlinear optical medium 12, due to the third-order opticalparametric effect induced by the propagation of the clockwise signalwave S_(R) and the pump waves P_(1R) and P_(2R), a clockwise FWM waveF_(R) having the carrier frequency ω_(f) (=ω_(P1) +ω_(P2) -ω_(S)) isgenerated (refer to FIG. 2B). Similarly, due to the third-orderparametric effect induced by the propagation of the counter-clockwisesignal wave S_(L) and the pump waves P_(1L) and P_(2L), acounter-clockwise FWM wave F_(L) having the carrier frequency ω_(f) isgenerated. The clockwise and counter-clockwise components again enterthe optical directional coupler 20 and produce interference.

In this case, although the signal waves S_(R), S_(L) and the pump wavesP_(1R), P_(2R), P_(1L) and P_(2L) undergo phase shift due to chromaticdispersion while propagating in the nonlinear optical medium 12 and thedispersive optical media 21, 22 and due to nonlinear effects (self-phasemodulation, cross-phase modulation) in the nonlinear optical medium 12,there is no phase shift difference between the counter-clockwise andclockwise waves themselves. Therefore, this optical circuit functionsessentially as a so-called optical loop mirror (refer to D. B.Mortimore, "Fiber loop reflectors", IEEE Journal of LightwaveTechnology, vol. 6, pp.1217-1224, 1988) to the signal wave S and thepump waves P₁, P₂, and in principle, 100% of the signal wave S and thepump waves P₁, P₂ is output to port 20a.

Here, the complex amplitude A_(fR) of a clockwise FWM wave F_(R)generated by the clockwise signal wave S_(R) and the clockwise pumpwaves P_(1R), P_(2R) (expressed by the expressions (1), (2) and (3)) isgiven by the following expression. ##EQU1##

Also, the complex amplitude A_(fL) of a counter-clockwise FWM wave F_(L)generated by the counter-clockwise signal wave S_(L) and thecounter-clockwise pump waves P_(1L), P_(2L) (expressed by theexpressions (4), (5) and (6)) is given by the following expression.##EQU2## where A_(S) * is the complex conjugate of A_(S) and C is thesquare root of the conversion efficiency given by an expression:(intensity of FWM wave/(intensity of signal wave S×intensity of pumpwave P₁ ×intensity of pump wave P₂)).

The complex amplitudes A_(d), A_(c) of the clockwise andcounter-clockwise FWM waves F_(R), F_(L), as each wave arrives at theports 20d, 20c through the respective dispersive optical medium 22, 21,are given by the following expressions. ##EQU3## where

    ΔK.sub.1 =K.sub.1 (ω.sub.S)+K.sub.1 (ω.sub.f)-K.sub.1 (ω.sub.P1)-K.sub.1 (ω.sub.P2)                 (11)

and

    ΔK.sub.2 =K.sub.2 (ω.sub.S)+K.sub.2 (ω.sub.f)-K.sub.2 (ω.sub.P1)-K.sub.2 (ω.sub.P2)                 (12).

In the optical directional coupler 20, the clockwise andcounter-clockwise FWM waves F_(R), F_(L) interfere, and the complexamplitudes A_(a), A_(b) of the FWM waves output from ports 20a, 20b aregiven by the following expressions. ##EQU4##

It follows that when the dispersive optical media 21, 22 fulfil thecondition that:

    ΔK.sub.2 L.sub.2 =ΔK.sub.1 L.sub.1 +(2n-1)π (15)

where n is an integer, then, in principle, 100% of FWM wave F can beoutput to port 20b, as illustrated in FIG. 2C.

The above results mean that it becomes possible to separate the FWM waveF generated in the nonlinear optical medium 12 from the signal wave Sand the pump waves P₁, P₂ without the use of such wavelength-divisiondemultiplexing means as wavelength filters.

Even when some optical noise is contained in the signal wave and thepump waves P₁, P₂, the optical noise is output together with the signalwave S and the pump waves P₁, P₂ from port 20a. There is no danger ofthe noise components becoming mixed in the FWM wave F.

It may be noted that taking into account certain allowable error α(0≦α<1/2)in expression (15), the following expression is obtained:

    ΔK.sub.2 L.sub.2 =ΔK.sub.1 L.sub.1 +(2n-1±α)π(16)

In this case, depending on the magnitude of the allowable error α, theoutput intensity level of FWM wave F output to port 20b is lowered;however, the signal wave S and the pump waves P₁, P₂ are never output toport 20b. Therefore, no problems can occur in practice.

When using a degenerate pump wave, the substitutions are made in theabove expressions such that ω_(P1) =ω_(P2), and A_(P1) =A_(P2). Also,when only one dispersive optical medium is being used, either L₁ or L₂in the above expressions is set equal to zero.

Variation 1 of Embodiment 1

The first variation of the Embodiment 1 of the FWM wave generationcircuit has the same circuit configuration as that shown in FIG. 1, inwhich ω_(S) and ω_(f) become symmetrical with respect to (ω_(P1)+ω_(P2))/2, and the generated FWM wave F becomes a phase conjugationwave of an input signal wave S. As shown in FIG. 3A, the carrierfrequencies of the signal wave S and the pump waves P₁, P₂ are relatedsuch that ω_(P1) <ω_(S) <ω_(P2) and ω_(S) =(ω_(P1) +ω_(P2))/2, then asshown in FIG. 3B, the carrier frequencies of the clockwise wave S_(R)and the FWM wave (phase conjugation wave) F_(R) become equal. The sameresult is produced with respect to the counter-clockwise signal waveS_(L). In this case (Variation 1 of Embodiment 1) also, the separationof the signal wave S and the FWM wave (phase conjugation wave) F ispossible according to the principle presented above (refer to FIG. 3C).

Variation 2 of Embodiment 1

Similarly, an example of using the degenerate wave in the parametriccircuit of FIG. 1 will be explained, i.e., the carrier frequenciesω_(P1) and ω_(P2) of the pump waves are such that ω_(P1) =ω_(P2) =ω_(P).

As shown in FIG. 4, when a signal wave S of carrier frequency ω_(S) andthe pump wave of carrier frequency ω_(P) are injected into port 20a ofthe optical directional coupler 20, an FWM wave F of carrier frequencyω_(f) (=2ω_(P) -ω_(S)) is generated in the nonlinear optical medium 12(refer to FIG. 5B). The FWM wave F is output from port 20b of theoptical directional coupler 20, while the signal wave S and the pumpwave P are output from port 20a of the optical directional coupler 20.

Variation 3 of Embodiment 1

Similarly in the optical parametric circuit of FIG. 1, a case ofinjecting signal waves S₁, S₂. . . S_(N) (carrier frequencies ω_(S1),ω_(S2), . . . ω_(SN)) multiplexed in the wavelength region and the pumpwaves P₁, P₂ of carrier frequencies ω_(P1), ω_(P2) into port 20a of theoptical directional coupler 20 will be explained. However, the intensityof each signal wave is chosen so as to be able to ignore the mutualnonlinear interaction of the signal waves.

As shown in FIG. 6, the wavelength-division multiplexed signal waves(WDM signal waves) S₁, S₂, . . . S_(N) and the pump waves P₁, P₂ (referto FIG. 7A) are separated to port 20c of the optical directional coupler20, and propagate successively through the dispersive optical medium21→nonlinear optical medium 12→dispersive optical medium 22→port 20d inthe clockwise direction. Here, the complex amplitude A_(SjR) of theclockwise jth signal wave S_(jR) of the clockwise WDM signal wavesS_(1R), . . . S_(NR) input from port 20c into the nonlinear opticalmedium 12 through the dispersive optical medium 21 is given by thefollowing expression.

    A.sub.SjR =A.sub.Sj ·exp (-iK.sub.1 (ω.sub.Sj)L.sub.1)(1')

In the meanwhile, the jth signal wave S_(j) of the WDM signal waves S₁,. . . S_(N) and the pump waves P₁, P₂ separated to port 20d of theoptical directional coupler 20 propagate through the dispersive opticalmedium 22→nonlinear optical medium dispersive optical medium 21→port20c, in the counter-clockwise direction. Here, the complex amplitudeA_(SjL) of the counter-clockwise jth signal wave S_(jL) input from port20d into the nonlinear optical medium 12 through the dispersive opticalmedium 22 is expressed as follows.

    A.sub.SjL =A.sub.Sj ·exp (-iK.sub.2 (ω.sub.Sj)L.sub.2 -iπ/2)                                                 (4')

The third-order parametric effect induced by the propagation of theclockwise jth signal wave S_(jR) and the pump waves P_(1R), P_(2R) inthe nonlinear optical medium 12, generates the jth FWM wave F_(jR) ofcarrier frequency ω_(fj) (=ω_(Pi) +ω_(P2) -ω_(Sj)) (refer to FIG. 7B).Similarly, the third-order parametric effect induced by the propagationof the counter-clockwise jth signal wave S_(jL) and the pump wavesP_(1L), P_(2L) generates the jth FWM wave F_(jL) of the carrierfrequency ω_(fj). These clockwise and counter-clockwise propagatingcomponents again enter the optical directional coupler 20 to produceinterference and, in principle, 100% of the jth signal wave S_(j) andthe pump waves P₁, P₂ is output to port 20a.

Here, the complex amplitude A_(fjR) of the clockwise jth FWM wave F_(jR)generated by the clockwise WDM signal wave S_(jR) and the pump wavesP_(1R), P_(2R) is expressed as follows.

    A.sub.fjR =C·A.sub.Sj *·A.sub.P1 ·A.sub.P2 ·exp [i(K.sub.1 (ω.sub.Sj)-K.sub.1 (ω.sub.P1)-K.sub.1 (ω.sub.P2))L.sub.1 ]                                (7')

Similarly, the complex amplitude Afj_(L) of the counter-clockwise jthFWM wave F_(jL) generated by the counter-clockwise jth signal waveS_(jL) and the pump waves P_(1L), P_(2L) is expressed as follows.

    A.sub.fjL =C·A.sub.Sj *·A.sub.P1 ·A.sub.P2 ·exp [i(K.sub.2 (ω.sub.Sj)-K.sub.2 (ω.sub.P1)-K.sub.2 (ω.sub.P2))L.sub.2 -iπ/2]                        (8')

The complex amplitudes A_(dj), A_(cj) of the clockwise andcounter-clockwise jth FWM waves F_(jR), F_(jL) upon arrival at ports20d, 20c through the dispersive optical media 22, 21 are given by thefollowing expressions.

    A.sub.dj =C·A.sub.Sj *·A.sub.P1 -A.sub.P2 ·exp [-i(K.sub.1 (ω.sub.fj)L.sub.1 +K.sub.2 (ω.sub.fj)L.sub.2)]·exp (iΔK.sub.1j L.sub.1)(9')

    A.sub.cj =C·A.sub.Sj *·A.sub.P1 -A.sub.P2 ·exp [-i(K.sub.1 (ω.sub.fj)L.sub.1 +K.sub.2 (ω.sub.fj)L.sub.2)]·exp (iΔK.sub.2j L.sub.2 -iπ/2)(10')

where

    ΔK.sub.1j =K.sub.1 (ω.sub.Sj)+K.sub.1 (ω.sub.fj)-K.sub.1 (ω.sub.P1)-K.sub.1 (ω.sub.P2)                 (11')

and

    ΔK.sub.2j =K.sub.2 (ω.sub.Sj)+K.sub.2 (ω.sub.fj)-K.sub.2 (ω.sub.P1)-K.sub.2 (ω.sub.P2)                 (12').

In the optical directional coupler 20, the clockwise andcounter-clockwise jth waves F_(jR), F_(jL) interfere, and the complexamplitudes A_(aj), A_(bj) of the jth FWM wave F_(j) output to ports 20a,20b are given by the following expressions.

    A.sub.aj ∝exp (iΔK.sub.2j L.sub.2)+exp (iΔK.sub.1j L.sub.1)                                                  (13')

    A.sub.bj ∝-exp (iΔK.sub.2j L.sub.2)+exp (iΔK.sub.1j L.sub.1)                                                  (14')

It follows that when the dispersive optical media 21, 22 fulfil thecondition that:

    ΔK.sub.2j L.sub.2 =ΔK.sub.1j L.sub.1 +(2n-1)π(15')

where n is an integer, then, in principle, 100% of the jth FWM waveF_(j) can be output to port 20b (refer to FIG. 7C), thus completelyseparating the jth signal wave S_(j), and the pump waves P₁, P₂therefrom.

By configuring the optical parametric circuit as demonstrated abovewhich uses the dispersive optical media 21, 22 satisfying the expression(15') for each j=1,2, . . . N, it becomes possible to completelyseparate the FWM waves F₁, . . . FN obtained by simultaneous wavelengthconversion of each wavelength of the WDM signal waves S₁, . . . S_(N),from the WDM signal waves S₁, . . . S_(N) and the pump waves P₁, P₂without the use of such wavelength separation means such as wavelengthfilters.

Also, if the carrier frequencies ω_(Sm), ω_(Sn) of the two signal wavesS_(m), S_(n) and the carrier frequencies ω_(P1), ω_(P2) of the pumpwaves P₁, P₂ are related in such a way to satisfy the equation:

    ω.sub.Sm +ω.sub.Sn =ω.sub.P1 +ω.sub.P2

then the carrier frequencies of the FWM waves F_(m), F_(n) are set toω_(Sn) and ω_(Sm), and wavelength interchange of the signal waves willbe obtained.

It may be noted that taking into account certain allowable error α(0≦α<1/2)in expression (15'), the following expression is obtained:

    ΔK.sub.2j L.sub.2 =ΔK.sub.1j L.sub.1 +(2n-1±α)π(16')

In this case, depending on the magnitude of the allowable error α, theoutput intensity level of the jth FWM wave F_(j) output to port 20b islowered; however, the WDM signal waves S₁, . . . S_(N), and the pumpwaves P₁, P₂ are never output to port 20b.

When using degenerate pump waves, the substitutions are made in theabove expressions such that ω_(P1) =ω_(P2), and A_(P1) =A_(P2). Also,when only one dispersive optical medium is being used, either L₁ or L₂in the above expressions is set equal to zero.

Variation 4 of Embodiment 1

The fourth variation of the Embodiment 1 of the FWM wave generationcircuit has the same circuit configuration as that shown in FIG. 6, inwhich the carrier frequencies ω_(S1), ω_(S2), . . . ω_(SN), ω_(P1),ω_(P2) of the WDM signal waves S₁, S₂, . . . S_(N) and the pump wavesP₁, P₂ satisfy the following expression:

    ω.sub.P1 <ω.sub.Sj <ω.sub.P2

for j=1,2, . . . N.

It should be noted that, in addition to the FWM wave F_(j) of a carrierfrequency ω_(P1) +ω_(P2) -ω_(Sj) generated in the nonlinear opticalmedium 12, unwanted FWM waves of carrier frequencies 2ω_(P1) -ω_(Sj),2ω_(P2) -ω_(Sj) are produced by the degenerate pump waves P₁, P₂, at aspacing |ω_(P1) -ω_(P2) |. If the carrier frequencies of the WDM signalwave S₁, S₂, . . . S_(N) and the pump waves P₁, P₂ satisfy theexpression ω_(P1) <ω_(Sj) <ω_(P2) (j=1,2, . . . N), as shown in FIG. 8A,the FWM wave F_(j) of carrier frequency ω_(P1) +ω_(P2) -ω_(Sj) excitedby the non-degenerate pump waves is generated between the frequenciesω_(P1), ω_(P2), as shown in FIG. 8B. The unwanted FWM waves excited bythe degenerate pump waves of carrier frequencies 2ω_(P1) -ω_(Sj),2ω_(P2) -ω_(Sj) are generated in a range outside the frequencies ω_(P1),ω_(P2). Thus, the wanted FWM waves can be readily separated from theunwanted FWM waves.

Variation 5 of Embodiment 1

A fifth variation is based similarly on the parametric circuit of FIG.1, in which a simultaneous wavelength conversion of WDM signal waves isperformed by utilizing the degenerate pump wave. Referring to FIG. 9,the pump wave P is the degenerate pump wave of carrier frequency ω_(P)=ω_(P1) =ω_(P2) which is injected into port 20a of the opticaldirectional coupler 20.

As shown in FIG. 9, when the WDM signal waves S₁, S₂, . . . S_(N) ofcarrier frequencies ω_(Sj) (j=1, 2, . . . N) and the pump wave P ofcarrier frequency ω_(P) (refer to FIG. 10A) are injected into port 20a,FWM waves F1, F₂, . . . F_(N) of carrier frequencies ω_(fj) (=2ω_(P)-ω_(Sj)) are produced in the nonlinear optical medium 12. The FWM wavesF1, F₂, . . . F_(N) are output from port 20b of the directional opticalcoupler 20 (refer to FIG. 10B), and the WDM signal waves S₁, S₂, . . .S_(N) and the pump wave P are output from port 20a.

Here, if the carrier frequencies ω_(Sm), ω_(Sn) of the two signal wavesS_(m), S_(n) and the carrier frequencies ω_(P) of the pump wave P arerelated in such a way to satisfy the equation:

    ω.sub.Sm +ω.sub.Sn =2ω.sub.P

then the carrier frequencies of the FWM waves F_(m), F_(n) are set toω_(Sn) and ω_(Sm), and wavelength interchange of the signal waves S_(m),S_(n) will be performed.

Embodiment 2

FIG. 11 shows a circuit configuration of Embodiment 2 of the opticalparametric circuit of the present invention.

The feature of Embodiment 2 is that the circuit components of FIG. 1 aremade as a polarization-maintaining type, that is, the opticaldirectional coupler 23, nonlinear optical medium 24 and the dispersiveoptical media 25, 26 are all polarization-maintaining devices. Thisconfiguration is also applicable to the phase conjugation generationcircuit presented in Variation 1 of the first embodiment, and thesimultaneous wavelength conversion circuit of the WDM signal wavespresented in Variation 2 of the first embodiment.

It should be noted that in the circuit of non-polarization-maintainingtype, changes in the polarization states of the signal wave(s) and thepump waves injected will cause the leakage of the signal wave(s) and thepump waves into the FWM wave(s) output from the circuit. Therefore, bymaking each component to be polarization-maintaining, it is possible tosuppress polarization crosstalk within the circuit and improve theisolation of the signal wave(s) and the pump waves with respect to theFWM wave(s). Such polarization-maintaining devices can be a birefringentmaterial such as polarization-maintaining optical fiber, and inputtingsignal wave(s) and pump waves polarized along the optic axis of thematerial will enable to preserve the polarization states of the opticalwaves in the optical circuit. In addition to suchpolarization-maintaining devices, it is effective in suppressing thepolarization crosstalk to insert single-polarization elements such aspolarizers, in input/output section or loop section of the circuit.

Variation 1 of Embodiment 2

FIG. 12 is an optical parametric circuit having a polarizationdispersion compensator 27, such as a birefringent waveguide, added tothe circuit shown in FIG. 11. It is also possible to apply the samecircuit configuration to the phase conjugation generation circuitpresented in Variation 1 of Embodiment 1 and the simultaneous wavelengthconversion circuit for WDM signal waves presented in Variation 3 ofEmbodiment 1.

Changes in the polarization state of the signal wave causes distortionsin the waveform of the output FWM wave(s) due to the birefringence(polarization dispersion) in the circuit components in the circuit ofpolarization-maintaining type. Also, when the conversion gains(expressed as a ratio of intensity of FWM wave to that of signal wave)in the two optic axes (polarization axes) of thepolarization-maintaining nonlinear optical medium are not the same,changes in polarization states in the input signal wave(s) will causevariations in the intensity of the output FWM wave(s). Therefore, apolarization dispersion compensator 27, such as a birefringent waveguideas shown in FIG. 12 is used to compensate the total polarizationdispersion in the circuit as shown in FIG. 11. By so doing, it ispossible to prevent waveform degradation of the FWM wave caused by thechanges in the polarization state of the signal wave.

The polarization compensator 27 is, as shown in this figure, disposed atthe FWM wave output section (port 23b of the optical directional coupler23), but it may also be disposed in the input path of the signal waveand at the injection section (port 23a of the coupler 23) of the signalwave or within the loop (between ports 23c and 23d of the coupler 23).Also, a method as disclosed in a U.S. Pat. No. 5,357,359 ("All-opticalpolarization independent optical time division multiplexer anddemultiplexer with birefringence compensation") may also be used, i.e.,the two components of each electrical field of the signal wave(s), pumpwaves and FWM wave(s) polarized along two optic axes of the circuitshown in FIG. 11 are interchanged from one optic axis to another opticaxis at points in the optical parametric circuit which compensate thetotal polarization dispersion within the circuit.

To equalize the conversion gain of the signal wave with respect to thetwo polarization axes of the polarization-maintaining nonlinear opticalmedium, when a polarization-maintaining nonlinear optical medium such aspolarization-maintaining optical fiber having the same conversion gainswith respect to the two polarization axes is used, the pump waves are tobe injected into each polarization axis at a 1:1 intensity ratio. Whenusing a device which exhibits two different conversion gains withrespect to the two polarization axes, such as semiconductor opticalamplifiers, it is necessary to adjust the intensity ratio of the pumpwaves so as to obtain the same conversion gain in each of thepolarization axes.

By so doing, it is possible to make the operation of the opticalparametric circuit polarization-insensitive.

Embodiment 3

FIG. 13 shows a circuit configuration of Embodiment 3 of the opticalparametric circuit of the present invention used as an FWM wavegeneration circuit provided with an optical multiplexer for coupling thesignal wave with the pump wave.

The feature of this embodiment is that a wavelength-division multiplexer11 has been provided, in front of port 20a of the optical directionalcoupler 20, to the circuit configuration shown in FIG. 1, for couplingthe signal wave S (shown in FIG. 14A) with the pump waves P₁, P₂ (shownin FIG. 14B). The carrier frequency ω_(f) of the output FWM wave F canbe tuned by selecting the carrier frequencies ω_(P1), ω_(P2) of the pumpwaves P₁, P₂. The circuit configuration of Embodiment 3 is applicable toboth the phase conjugation generation circuit presented in Variation 1of Embodiment 1 as well as to the simultaneous wavelength conversioncircuit for WDM signal waves presented in Variation 3 of Embodiment 1.

Embodiment 4

FIG. 15 shows a circuit configuration of Embodiment 4 of the opticalparametric circuit of the present invention used as an FWM wavegeneration circuit for blocking the return signal wave and the pumpwaves.

The feature of this embodiment is that a blocking device has beenprovided to the circuit of FIG. 1 at port 20a of the optical directionalcoupler 20 for blocking the signal waves S and the pump waves P₁, P₂which are output from port 20a of the optical directional coupler 20.The circuit configuration of Embodiment 4 is also applicable to both thephase conjugation generation circuit presented in Variation 1 ofEmbodiment 1 as well as to the simultaneous wavelength conversioncircuit for WDM signal waves presented in Variation 3 of Embodiment 1.

The signal wave S and the pump waves P₁, P₂ return to input port 20a,thus very high intensity pump waves P₁, P₂ could exert undesirableinfluence on the generators for signal wave and pump waves. Therefore,the blocking device 28 is disposed in front of port 20a of the opticaldirectional coupler 20 to block the returning signal wave S and the pumpwaves P₁, P₂ which are output from port 20a. The blocking device 28could be an optical isolator or an optical circulator.

Embodiment 5

FIG. 16 shows a circuit configuration of a fifth embodiment of theoptical parametric circuit of the present invention provided with adevice for suppressing unwanted wave components leaking into the outputFWM wave.

The feature of this embodiment is that a filtering device has beenprovided to the circuit of FIG. 1 after port 20b of the opticaldirectional coupler 20 for suppressing the unwanted signal waves leakinginto the FWM wave F output from port 20b of the optical directionalcoupler 20. The circuit configuration of Embodiment 5 is also applicableto both the phase conjugation generation circuit presented in Variation1 of Embodiment 1 as well as to the simultaneous wavelength conversioncircuit for WDM signal waves presented in Variation 3 of Embodiment 1.

The reasons for causing leaking of signal waves(s) and pump waves intooutput FWM wave(s) are, for example, asymmetry in the splitting ratio(other than 50:50) of the optical directional coupler 20 andpolarization crosstalk between signal wave S and pump waves P₁, P₂ whichmay occur in the optical directional coupler 20, nonlinear opticalmedium 12 and dispersive optical media 21, 22. Other possibilitiesinclude the unwanted FWM waves of carrier frequencies 2ω_(P1) -ω_(S),2ω-ω_(S) generated simultaneously when generating FWM waves of carrierfrequencies ω_(f) (=ω_(P1) +ω_(P2) -ω_(S)) from the signal waves andpump waves of carrier frequencies ω_(S), ω_(P1), ω_(P2), respectively.

To suppress the output of unwanted waves from port 20b, the circuitshown in FIG. 16 provides a wavelength filter 13 which passes only thewavelengths having carrier frequencies ω_(f) at port 20b of the opticaldirectional coupler 20 for generating FWM wave F.

Embodiment 6

Embodiment 6 of the optical parametric circuit is an application to anoptical phase conjugation circuit using angular-modulated pump waves orto a simultaneous wavelength conversion of WDM signal waves usingangular-modulated pump waves.

The feature of this embodiment is to perform phase modulation orfrequency modulation of two pump waves P₁, P₂ in the circuits shown inVariation 1 of Embodiment 1 and Variation 4 of Embodiment 1.

When cw pump waves with narrow spectral widths are used, nonlinearback-scattering waves, which are caused by stimulated Brillouinscattering or induced diffraction grating generated in the nonlinearoptical medium 12 and the dispersive optical media 21, 22, are outputfrom port 20b of the directional optical coupler 20. According to thisembodiment, by performing angular modulation to widen the spectralbandwidth of the pump waves, the threshold intensity of the pump wavesfor causing back-scattering is increased, thereby permitting the use ofhigher intensity pump waves.

Especially, as shown in FIGS. 17A and 18A, when angular modulationswhich are mutually conjugate are applied to the two pump waves, theinstantaneous carrier frequency (ω_(P1) +ω_(P2))/2 is held constant,thereby preventing variations in the carrier frequencies of thegenerated FWM wave F (or F_(j)). This is demonstrated in FIGS. 17B and18B. In FIGS. 18A and 18B, filled and unfilled circles are used forshowing the correspondence between the WDM signal waves and the FWMwaves.

In general, if the amount of angular modulation of the signal wave isdenoted by φ_(S) (t) (or φ_(Sj) (t)) and the angular modulations of thepump waves by φ_(P1) (t) and φ_(P2) (t), and when they are related as inthe following expression:

    φ.sub.P1 (t)+φ.sub.P2 (t)-φ.sub.S (t)=0(or φ.sub.P1 (t)+φ.sub.P2 (t)-φ.sub.Sj (t)=0)

it is possible to prevent variations in the carrier frequencies of theFWM waves generated.

Embodiment 7

Embodiment 7 of the optical parametric circuit is an application to aphase conjugation generation circuit or a simultaneous wavelengthconversion of WDM signal waves using intensity-modulated pump waves.

The feature of the circuit of this embodiment is the addition ofintensity modulation to provide intensity modulations synchronized tothe signal wave S (or WDM signal waves S₁, . . . S_(N)) to the two pumpwaves P₁, P₂ in the circuits of Variation 1 of Embodiment 1 andVariation 4 of Embodiment 1.

According to the circuit of this embodiment, it is also possible toprevent the generation of back-scattering waves as in the circuitpresented in Embodiment 6. FIG. 19 corresponds to FIG. 17A, and FIG. 20corresponds to FIG. 18A, respectively, for Embodiments 6 and 7. In thisembodiment, it is possible to raise the peak intensity of the pump waveswhile keeping the average intensity of the pump waves constant.

It is also permissible to use combined modulation of the intensitymodulation presented in this embodiment and the angular modulationpresented in Embodiment 6.

The actual example of the operation of the phase conjugation generationcircuit of the present invention will be explained with reference toFIG. 21. In the circuit of this example, polarization-maintainingoptical fibers are used to serve as the nonlinear optical medium 24 andthe dispersive optical medium 25 (both of which components arepolarization-maintaining types). Also, phase modulation to the two pumpwaves P₁, P₂ is performed. Time-resolved spectra for the signal wave Sand the pump waves P₁, P₂ injected into port 23a of the opticaldirectional coupler 23 are shown in observed image (a). In observedimage (b) are shown time-resolved spectra of the phase conjugation wave(FWM wave) F output from port 23b of the optical directional coupler 23.It is demonstrated that it is possible to generate phase conjugationwave F having the same wavelength as that of the signal wave S.

Together with the image of the phase conjugation wave F presented in theobserved image (b), an image H₁ is seen at the same wavelength as thepump wave P₂. The image H₁ is generated from a wavelength conversion ofpump wave P₁ caused by signal wave S acting as the degenerate pump wave,and appears at port 23b of the directional optical coupler 23.Similarly, an image H₂ is seen at the same wavelength as the pump waveP₁. The image H₂ is generated from a wavelength conversion of pump waveP₂ caused by signal wave S acting as the degenerate pump wave, andappears at port 23b of the directional optical coupler 23. The images H₁and H₂ both have different wavelengths from that of the phaseconjugation wave F, and therefore, they can readily be eliminated usingwavelength filters.

Embodiment 8

FIG. 22 shows a circuit configuration of Embodiment 8 which is anapplication of the parametric circuit to a dual-input optical gatecircuit (optical AND-circuit).

The feature of the circuit of this embodiment is that the dual-inputsingle-output optical gate circuit (optical AND-circuit) is realized bycoupling of an optical input signal S_(in) with an optical gate signal Gwith the use of a wavelength-division multiplexer 11, which is input,through an optical isolator 28 into port 20a of the optical directionalcoupler 20.

In this embodiment, the optical input signal S_(in) (refer to FIG. 23A)is a pulsed signal wave S of carrier frequency the optical gate signal G(refer to FIG. 23B) is a pulsed pump wave P of carrier frequency up andthe optical output signal S_(out) is the FWM wave F of carrier frequencyω_(f) (=2ω_(P) -ω_(S)). When the optical input signal S_(in) and theoptical gate signal G are input into the nonlinear optical medium 12 soas to overlap each other, an optical output signal S_(out) is generatedin a timeslot t₂ (refer to FIG. 23C), and the optical output signalS_(out) is output from port 20b (refer to FIG. 23D). However, it isnoted that a wavelength conversion (ω_(S) →ω_(f)) takes place in theoptical gate circuit of this embodiment.

Variation 1 of Embodiment 8

FIG. 24 shows a first variation of Embodiment 8, which is an applicationof the parametric circuit to a triple-input optical gate circuit(optical AND-circuit).

The feature of the circuit of this variation is to present atriple-input one-output optical gate circuit (optical AND-gate) whichdoes not result in wavelength conversion while using the same opticalgate circuit shown in FIG. 22.

In this embodiment, the optical input signal S_(in) (refer to FIG. 25A)of carrier frequency ω_(S) is related to the carrier frequencies ω_(P1),ω_(P2) of optical gate signals G₁, G₂ which are modulated as shown inFIG. 25B by the following expression.

    2ω.sub.S =ω.sub.P1 +ω.sub.P2

When the optical input signal S_(in) and the optical gate signals G₁, G₂are input into the nonlinear optical medium 12 so as to overlap eachother, the carrier frequency of the generated FWM wave F becomes ω_(S),that is, the carrier frequencies of the optical input signal S_(in) andthe optical output signal S_(out) become the same (refer to FIG. 25C).The optical input signal S_(in) input into port 20a of the opticaldirectional coupler 20 together with optical gate signals G₁, G₂ isoutput again from port 20a. On the other hand, the optical output signalS_(out) of carrier frequency ω_(S) is output from port 20b of theoptical directional coupler 20 (refer to FIG. 25D).

Embodiment 9

FIG. 26 shows the circuit configuration of Embodiment 9 which is anapplication of the parametric circuit to an optical time-divisiondemultiplexer.

The feature of this embodiment is that, by connecting optical gatecircuits shown in FIG. 22 in a multi-stage configuration, an opticaltime-division demultiplexer is realized for separating a time-divisionmultiplexed (TDM) optical signal.

In this embodiment, the first-stage optical gate circuit demultiplexestwo channels; wherein a TDM optical input signal S_(in) which is apulsed signal wave of carrier frequency ω_(S) and which contains fourchannels in the timeslots (t₁, t₂, t₃, t₄) (refer to FIG. 27A) and anoptical gate signal G₁ which is a pulsed pump wave of carrier frequencyω_(P) and which is active in the timeslots (t₂, t₄) (refer to FIG. 27B)are input, and an optical output signal S_(out1) which is a generatedFWM wave of carrier frequency ω_(f) (=2ω_(P) -ω_(S)) in the respectivetimeslots (t₂, t₄) is output (refer to FIG. 27C).

In the second-stage optical gate circuit, an optical input signal whichis the optical output signal S_(out1) of the first-stage optical gatecircuit and an optical gate signal G₂ which is a pulsed pump wave ofcarrier frequency ω_(P) and which is active in the timeslots (t₃, t₄)(refer to FIG. 27D) are input, and an optical pulse signal S_(out2)which is a generated FWM wave of carrier frequency ω_(S) (=2ω_(P)-ω_(f)) in the timeslot (t₄) is output (refer to FIG. 27E). Theprocedure is able to demultiplex the TDM optical input signal S_(in) toextract one channel in the timeslot in which both optical gate signalsG₁, G₂ are active.

It should be noted that in the first-stage optical gate circuit, the TDMoptical input signal S_(in) of carrier frequency ω_(S) generates anoptical output signal (FWM wave) S_(out1) of carrier frequency ω_(f).Similarly, in the second-stage optical gate circuit, the optical inputsignal (the optical input signal S_(out1)) of carrier frequency ω_(f)generates an optical output signal (FWM wave) S_(out2) of carrierfrequency ω_(S). Accordingly, this circuit of Embodiment 9 functions inthe same way as the triple-input optical gate circuit of Variation 1 ofEmbodiment 8 in which the carrier frequencies remain in an optical inputsignal and an optical output signal as a whole, while the circuit ofEmbodiment 9 has the advantage of requiring only one carrier frequencyω_(P) for the optical gate signals G₁ and G₂.

It is also permissible to apply the multi-stage configuration to thetriple-input optical gate circuit of Variation 1 of Embodiment 8 (referto FIG. 24).

Embodiment 10

FIG. 28 shows the circuit configuration of Embodiment 10 which is anapplication of the parametric circuit to another type of opticaltime-division demultiplexer.

The feature of this embodiment is that, by combining the gate circuit ofFIG. 22 with a 1-input, 4-output wavelength-division demultiplexer 49,it is possible to present an optical time-division demultiplexer forsimultaneous separation of four channels of time-division multiplexedoptical pulse signals.

In the circuit of FIG. 28, a TDM optical input signal S_(in) of carrierfrequency ω_(S) which contains four channels in the timeslots (t₁, t₂,t₃, t₄) (refer to FIG. 29A) is input together with optical gate signalsG₁, G₂, G₃, G₄ which are respectively active in the timeslots (t₁, t₂,t₃, t₄) at different carrier frequencies ω_(P1), ω_(P2), ω_(P3), ω_(P4)(refer to FIG. 29B), and optical output signals S_(out1), S_(out2),S_(out3), S_(out4) of different carrier frequencies ω_(f1), ω_(f2),ω_(f3), ω_(f4) are output (refer to FIG. 29C) which are generated indegenerate four-wave mixing process between the TDM optical input signalS_(in) and each of the optical gate signals G₁, G₂, G₃, G₄, where ω_(fk)=2ω-ω_(S) (k=1, . . . 4). The respective optical output signalsS_(out1), S_(out2), S_(out3), S_(out4) are separated in thewavelength-division demultiplexer 29 into individual channels of carrierfrequencies ω_(f1), ω_(f2), ω_(f3), ω_(f4), thereby achieving asimultaneous separation of four channels (refer to FIG. 29D).

In this case, for k=1, 2, 3, 4, it is assumed that the relationship ofthe frequencies is given by the following expression.

    {K.sub.2 (ω.sub.S)+K.sub.2 (ω.sub.fk)-2K.sub.2 (ω.sub.Pk)}L.sub.2 ={K.sub.1 (ω.sub.S)+K.sub.1 (ω.sub.fk)-2K.sub.1 (ω.sub.Pk)}L.sub.1 +(2n-1±α)π

In the optical time-division demultiplexers shown above, it is alsopermissible to use non-degenerate pump waves optical gate signals.

Embodiment 11

FIG. 30A is a schematic diagram of the optical parametric circuit ofEmbodiment 11 of the present invention, showing the flow of opticalwaves.

In this embodiment, a signal wave S (refer to FIG. 31A) of carrierfrequency ω_(S) is injected into port 20b of the optical directionalcoupler 20, and is divided into ports 20c, 20d at equal intensities andpolarization states, respectively. The phase of the signal wave S_(R)output from port 20c, which is a cross port of port 20b, is retarded by90 degrees with respect to that of the signal wave S_(L) output fromport 20d which is the through port of port 20b. Therefore, designatingthe complex amplitude of the output signal wave S_(L) at port 20d byA_(S), the complex amplitude of the signal wave S_(R) at port 20c isgiven by A_(S) ·exp(-iπ/2).

The pump waves P₁, P₂ (refer to FIG. 31B) of carrier frequencies ω_(P1),ω_(P2) are injected into port 20a of the optical directional coupler 20,and are divided into ports 20c, 20d at equal intensities andpolarizations. However, the phases of the pump waves P_(1L), P_(2L)output from the cross port 20d are retarded by 90 degrees from thephases of the pump waves P_(1R), P_(2R) output from the through port20c, respectively. Therefore, designating the complex amplitudes of thepump waves P_(1R), P_(2R) at port 20c by A_(P1), A_(P2) the complexamplitudes of the pump waves P_(1L), P_(2L) at port 20d is given byA_(P1) ·exp(-iπ/2) and A_(P2) ·exp(-π/2), respectively.

Accordingly, the signal wave S_(R) and the pump waves P_(1R), P_(2R)(refer to FIG. 31C) output to port 20c of tile directional coupler 20propagate in the direction of the dispersive optical medium 21→nonlinearoptical medium 12→dispersive optical medium 22→port 20d, i.e. in theclockwise direction. Here, the complex amplitudes A_(SR), A_(P1R), andA_(P2R) of the clockwise signal S_(R) and the clockwise pump wavesP_(1R), P_(2R) which are input from port 20c via dispersive opticalmedium 21 into nonlinear optical medium 12 are expressed as follows.

    A.sub.SR =A.sub.S ·exp (-iK.sub.1 (ω.sub.S)L.sub.1 -iπ/2)(17)

    A.sub.P1R =A.sub.P1 ·exp (-iK.sub.1 (ω.sub.P1)L.sub.1)(18)

    A.sub.P2R =A.sub.2 ·exp (-iK.sub.1 (ω.sub.P2)L.sub.1)(19)

In the meanwhile, the signal wave S_(L) and the pump waves P_(1L),P_(2L) output to port 20d of the directional coupler 20 propagate in thedirection of the dispersive optical medium 22→nonlinear optical medium12→dispersive optical medium 21→port 20c, i.e. in the counter-clockwisedirection. Here, the complex amplitudes A_(SL), A_(P1L) and A_(P2L) ofthe counter-clockwise signal S_(L) and the counter-clockwise pump wavesP_(1L), P_(2L) which are input from port 20d via dispersive opticalmedium 22 into nonlinear optical medium 12 are expressed as follows.

    A.sub.SL =A.sub.S ·exp (-iK.sub.2 (ω.sub.S)L.sub.2)(20)

    A.sub.P1L =A.sub.P1 ·exp (-iK.sub.2 (ω.sub.P1)L.sub.2 -iπ/2)                                                 (21)

    A.sub.P2L =A.sub.P2 ·exp (-iK.sub.2 (ω.sub.P2)L.sub.2 -iπ/2)                                                 (22)

Within the nonlinear optical medium 12, due to the third-order opticalparametric effect induced by the propagation of the clockwise signalwave S_(R) and the clockwise pump waves P_(1L) and P_(2L), the signalwave S_(R) is amplified and a clockwise FWM wave F_(R) having thecarrier frequency ω_(f) (=ω_(P1) +ω_(P2) -ω_(S)) is generated (refer toFIG. 31D). Similarly, due to the third-order parametric effect inducedby the propagation of the counter-clockwise signal wave S_(L) and thecounter-clockwise pump waves P_(1L) and P_(2L), the signal wave S_(L) isamplified and a counter-clockwise FWM wave F_(L) having the carrierfrequency ω_(f) is generated. The clockwise and counter-clockwise wavecomponents again enter the directional optical coupler 20 and produceinterference.

The circuit of this embodiment also functions as an optical loop mirrorwith respect to the signal waves S and the pump waves P₁, P₂ ;therefore, in principle, 100% of the amplified signal wave S' is outputto port 20b and the pump waves P₁ and P₂ to port 20a, to enable theresult of a complete separation of the amplified signal waves S', andthe pump waves P₁ and P₂.

Here, the complex amplitude A_(fR) of a clockwise FWM wave F_(R)generated by the clockwise signal wave S_(R) and the clockwise pumpwaves P_(1R), P_(2R) (expressed by the expressions (17), (18) and (19))is given by the following expression. ##EQU5##

Also, the complex amplitude A_(fL) of a counter-clockwise FWM wave F_(L)generated by the counter-clockwise signal wave S_(L) and thecounter-clockwise pump waves P_(1L), P_(2L) (expressed by theexpressions (20), (21) and (22)) is given by the following expression.##EQU6## where C is the square root of the conversion efficiencypreviously explained above.

The complex amplitudes A_(d), A_(c) of the clockwise andcounter-clockwise FWM waves F_(R), F_(L), as each wave arrives at theports 20d, 20c through the respective dispersive optical medium 22, 21,are given by the following expressions. ##EQU7## where ΔK₁, ΔK₂ are thesame as the expressions given in (11) and (12).

In the optical directional coupler 20, the clockwise andcounter-clockwise FWM waves F_(R), F_(L) interfere, and the complexamplitudes A_(a), A_(b) of the FWM waves output to the ports 20a, 20bare given by the following expressions. ##EQU8##

It follows that when the dispersive optical media 21, 22 fulfil thecondition that:

    ΔK.sub.2 L.sub.2 =ΔK.sub.1 L.sub.1 +2nπ     (29)

where n is an integer, then, in principle, 100% of FWM wave F can beoutput to port 20b with the amplified signal wave S' (refer to FIG.31E), thus completely isolating the pump waves P₁, P₂ (which are outputto port 20a) therefrom.

Meanwhile, FIG. 30B shows the state of propagation of the waves when thedispersive optical media 21, 22 satisfy the following condition.

    ΔK.sub.2 L.sub.2 =ΔK.sub.1 L.sub.1 +(2n-1)π (30)

where n is an integer. In this case, 100% of the FWM wave F is output toport 20a together with pump waves P₁, P₂ (refer to FIG. 31F) inprinciple, and the amplified signal wave S' is output to port 20b (referto FIG. 31G). This means that the amplified signal wave S' is completelyseparated from the FWM wave F and the pump waves P₁, P₂.

By configuring the optical parametric circuit as demonstrated above,when selecting the dispersive optical media 21, 22 to satisfy theexpression (29), it becomes possible to separate the FWM wave Fgenerated and the amplified signal wave S' from the pump waves P₁, P₂without the use of such wavelength-division demultiplexing means aswavelength filters. On the other hand, when selecting the dispersiveoptical media 21, 22 to satisfy the expression (30), it becomes possibleto separate the amplified signal wave S' from the FWM wave F and thepump waves P₁, P₂. This aspect of the circuit operation will beexplained later in another embodiment.

It may be noted that taking into account certain allowable error α(0≦α<1/2)in expression (29), the following expression is obtained.

    ΔK.sub.2 L.sub.2 =ΔK.sub.1 L.sub.1 +(2n-1±α)π(31)

In this case, depending on the magnitude of the allowable error α, theoutput intensity level of FWM wave F output to port 20b is lowered;however, the pump waves P₁, P₂ are never output to port 20b. Therefore,no problems can occur in practice.

Even when some optical noise is contained in the pump waves P₁, P₂, theoptical noise is output together with the pump waves P₁, P₂ from port20a, the optical noise becomes never mixed in the amplified signal waveS' and the FWM wave F.

Variation 1 of Embodiment 11

FIG. 32 presents a first variation of Embodiment 11 in which adegenerate pump wave (carrier frequency ω_(P) =ω_(P1) =ω_(P2)) is usedin the circuit of Embodiment 11.

In this embodiment, when a signal wave S shown in FIG. 31A is injectedfrom port 20b of the optical directional coupler 20, and the pump wave P(refer to FIG. 33A) of carrier frequency ω_(P) is injected from port20a, an FWM wave F_(R) of carrier frequency ω_(f) (=2ω_(P) -ω_(S)) isgenerated. FIG. 33B shows the generated FWM wave F_(R), the amplifiedsignal wave S_(R) ', and the pump wave P_(R) which are output from thenonlinear optical medium 12 in the clockwise direction. The same effectoccurs in the counter-clockwise direction. The FWM wave F and theamplified signal wave S' are output from port 20b, and the pump wave Pfrom port 20a of the optical directional coupler 20.

The following embodiments are all explained in the case that the pumpwave P is degenerate.

As in the first embodiment, in place of a signal wave S, WDM signalwaves S₁, S₂, . . . S_(N) of carrier frequencies ω_(S1), ω_(S2), . . .ω_(SN) can be used to separate the WDM FWM wave F_(j) and the signalwave from the pump waves. As in the case presented in Embodiment 2 andshown in FIG. 11, polarization-maintaining type configuration can beused to suppress polarization crosstalk within the circuit to improvethe isolation of the pump waves with respect to the amplified signalwave S' and the FWM wave F. Further, by providing polarizationcompensating means as in the case of Variation 1 of Embodiment 2,polarization-insensitivity can be achieved. In the cases of theembodiments to follow, it is also possible to suppress polarizationcrosstalk by using polarization-maintaining type components.

Embodiment 12

FIG. 34 shows a configuration of the optical parametric circuit ofEmbodiment 12.

The feature of this embodiment is to block the return pump wave P outputfrom port 20a of the optical directional coupler 20 in the basicconfiguration presented in Embodiment 11.

In the parametric circuit of this embodiment, the pump wave P returns tothe input port 20a. Therefore, very high intensity pump wave P couldexert undesirable influence on the generator for the pump wave. Anoptical isolator 28 is disposed in front of port 20a of the opticaldirectional coupler 20 for injection of the pump wave P to block thepump wave P output from port 20a. An optical isolator 28 may be replacedwith an optical circulator.

Embodiment 13

FIG. 35 shows a configuration of the optical parametric circuit ofEmbodiment 13.

The feature of this embodiment is to separate the signal wave S inputinto port 20b of the optical directional coupler 20 from the amplifiedsignal wave S' and FWM wave F output from port 20b of the opticaldirectional coupler 20 in the basic configuration presented inEmbodiment 11.

In this optical parametric circuit, because an input signal wave S andan output signal wave S' and FWM wave F all pass through the same port20b of the optical directional coupler 20, a means for separating themis necessary. This is achieved by disposing an optical circulator 38 onport 20b of the optical directional coupler 20 to separate the amplifiedsignal wave S' and the FWM wave F from the input signal wave S.

Embodiment 14

Embodiment 14 is presented in two versions: 14A and 14B.

Embodiment 14A

FIG. 36 shows a configuration of the optical parametric circuit ofEmbodiment 14A as an optical amplifier.

In this embodiment, in addition to the configuration of Embodiment 13, awavelength filter 29 is used, which blocks FWM wave F and passes onlythe amplified signal wave S' (of carrier frequency ω_(S)). The pump waveP (of carrier frequency ω_(P)) may be either a cw (continuous wave) waveor an intensity-modulated wave synchronized with the signal wave S. Whena signal wave S is injected into port 20b of the optical directionalcoupler 20 through the optical circulator 38, an amplified signal waveS' (refer to FIG. 37) is output from port 20b through the opticalcirculator 38 and the wavelength filter 29.

Embodiment 14B

FIG. 38 shows another configuration of the optical parametric circuit asan optical amplifier in Embodiment 14B.

The feature of this embodiment is the selection of propagation constantsK₁ (ω) and K₂ (ω) and the lengths L₁ and L₂ of the respective dispersiveoptical media 21, 22 (expressed in Equation (30)) so that only anamplified signal wave S' is output from port 20b of the opticaldirectional coupler 20, and separated from an FWM wave F and the pumpwave P which are output from port 20a (refer to FIG. 39). Therefore, thewavelength filter 29 used in FIG. 36 to pass the amplified signal waveS' and suppress FWM wave F is unnecessary in principle.

In this embodiment, an optical circulator 38 is used to separate theamplified signal wave S' output from port 20b of the optical directionalcoupler 20 from the signal wave S input into port 20b of the opticaldirectional coupler 20.

Embodiment 15

FIG. 40A shows a circuit configuration of the optical parametric circuitapplied to an FWM wave generation circuit in Embodiment 15.

In this embodiment, a wavelength filter 13 which passes only FWM waves Fhas been added to the circuit which was presented in Embodiment 13 andshown in FIG. 35. When a signal wave S (carrier frequency ω_(S)) isinput via the optical circulator 38 into port 20b of the opticaldirectional coupler 20, an FWM wave F is output from port 20b throughthe optical circulator 38 and the wavelength filter 13 (refer to FIG.41). The carrier frequency ω_(f) (=2ω_(P) -ω_(S)) of the FWM wave F canbe tuned by selecting the carrier frequency up of the pump wave P.

As shown in FIG. 40B, it is permissible to replace the opticalcirculator 38 and the wavelength filter 13 with a wavelength-divisiondemultiplexer 30 which separates the FWM wave of carrier frequency ω_(f)from the signal waves S, S' of carrier frequency ω_(S).

In Embodiments 14 and 15, even if the pump wave P leaks into port 20b,the wavelength filters 29, 13 are able to filter the leaked pump wave P,therefore, the isolation of pump wave P with respect to the FWM wave Fis further enhanced. It is also permissible to dispose an additionalwavelength filter which suppresses the pump wave P. If the circuit is tobe a polarization-maintaining type, a polarizer is also effective insuppressing the leak of pump waves caused by polarization crosstalk tofurther enhance the performance.

Embodiment 16

Embodiment 16 is an application of the circuit presented in Embodiment15 to a 2-input 1-output optical gate circuit (optical AND-circuit).FIG. 42 shows the flow of optical signals in the circuit.

In this embodiment, an optical input signal S_(in) is input into port20b of the optical directional coupler via the optical circulator 38 andan optical gate signal G is input into port 20a, where the optical inputsignal S_(in) is a pulsed signal wave of carrier frequency ω_(S) (referto FIG. 43A) and the optical gate signal G is a pulsed pump wave ofcarrier frequency ω_(P) (refer to FIG. 43B). Then, an optical outputsignal S_(out) which is an FWM wave of carrier frequency ω_(f) (=2ω_(P)-ω_(S)) is produced and the optical input signal S_(in) ' is amplifiedin the timeslots (t₂) in which the optical input signal S_(in) and theoptical gate signal G overlap each other in the nonlinear optical medium12. FIG. 43C shows these optical signals in the clockwise direction. Theoptical output signal S_(out) and the amplified optical input signalS_(in) ' are separated from the optical gate signal G and output fromport 20b of the optical directional coupler 20 (refer to FIG. 43D). Thesignals S_(out) and S_(in) ' then pass through the optical circulator 38and are further filtered with a wavelength filter 13 so as to block theamplified optical input signal S_(in) ' and to output only the opticaloutput signal S_(out) (refer to FIG. 43E). Therefore, this circuit hasthe same function as the circuit explained in Embodiment 8 and shown inFIG. 22.

Variation 1 of Embodiment 16

FIG. 44 shows a circuit configuration of a Variation 1 of Embodiment 16.This is an application of the optical parametric circuit to an opticaltime-division demultiplexer for separating a TDM signal, by connectingoptical gate circuits shown in FIG. 42 in a multi-stage configuration.

In this variation, in the first-stage optical gate circuit, a TDMoptical input signal S_(in) which is a pulsed signal wave of carrierfrequency ω_(S) and which contains four channels in the timeslots (t₁,t₂, t₃, t₄) (refer to FIG. 45A) and an optical gate signal G₁ which is apulsed pump wave of carrier frequency ω_(P) and which is active in thetimeslots (t₂, t₄) (refer to FIG. 45B) are input, and an optical outputsignal S_(out1) which is a generated FWM wave of carrier frequency ω_(f)(=2ω_(P) -ω_(S)) in the respective timeslots (t₂, t₄) (refer to FIG.45C) is output via a wavelength filter 13 which passes only the carrierfrequency ω_(f) to block the amplified optical input signal S_(in) '(refer to FIG. 45F).

In the second-stage optical gate circuit, a optical input signal whichis the optical output signal S_(out1) from the first-stage optical gatecircuit and an optical gate signal G₂ which is a pulsed pump wave ofcarrier frequency ω_(P) and which is active in the timeslots (t₃, t₄)(refer to FIG. 45D) are input, and an optical output signal S_(out2)which is a generated FWM wave of carrier frequency ω_(S) (=2ω_(P)-ω_(f)) in the timeslot (t₄) is output via a wavelength filter 29 whichpasses only the carrier frequency ω_(S) to block the amplified opticalinput signal S_(out1) ' (refer to FIG. 45E).

The procedure enables to demultiplex the TDM optical input signal S_(in)to extract one channel in the timeslot in which both optical gatesignals G₁ and G₂ are active, and presents the same function as thecircuit of Embodiment 9.

Variation 2 of Embodiment 16

FIG. 46 shows a circuit configuration of a Variation 2 of Embodiment 16.The feature of this configuration is that the wavelength filters 13, 29in the optical time-division demultiplexer presented in FIG. 44 arereplaced with wavelength-division demultiplexers 30₁, 30₂.

In this variation, in the first-stage optical gate circuit, a TDMoptical input signal S_(in) of carrier frequency ω_(S) which containsfour channels in the timeslots (t₁, t₂, t₃, t₄) (same as is shown inFIG. 45A) and an optical gate signal G₁ of carrier frequency ω_(P) whichis active in the timeslots (t₂, t₄) (same as is shown in FIG. 45B) areinput, and an optical output signal S_(out1) which is a generated FWMwave of carrier frequency ω_(f) (=2ω_(P) -ω_(S)) in the correspondingtimeslots (t₂, t₄) (same as is shown in FIG. 45C) is output togetherwith the optical input signal S_(in) ' amplified in the correspondingtimeslots (t₂, t₄) (same as is shown in FIG. 45F) from an opticalcirculator 38₁ to a wavelength-division demultiplexer 30₁ whichseparates the optical output signal S_(out1) of carrier frequency ω_(f)from the amplified optical input signal S_(in) ' of carrier frequencyω_(S). The first-stage optical gate circuit, therefore, achieves theisolation of the two timeslots (t₂, t₄) of the TDM optical input signalS_(in).

In the second-stage optical gate circuit, an optical input signal whichis the amplified optical output signal S_(in), output from thefirst-stage optical gate circuit and an optical gate signal G₂ ofcarrier frequency ω_(P) which is active in the timeslots (t₁, t₃) (referto FIG. 47A) are input, and an optical output signal S_(out2) which is agenerated FWM wave of carrier frequency ω_(f) (=2ω_(P) -ω_(S)) in thetimeslots (t₁, t₃) (refer to FIG. 47B) is output with the optical inputsignal S_(in) " amplified in the corresponding timeslots (t₁, t₃) froman optical circulator 38₂ to a wavelength-division demultiplexer 30₂which separates the optical output signal S_(out2) of carrier frequencyω_(f) from the amplified optical input signal S_(in) " of carrierfrequency ω_(S). The second-stage optical gate circuit, therefore,achieves the isolation of the two timeslots (t₁, t₃) of the TDM opticalinput signal S_(in).

The procedure enables to demultiplex the TDM optical input signal S_(in)to extract channels in the timeslots in which respective optical gatesignals G₁ and G₂ are active. The amplified optical input signal S_(in)" output from the second-stage circuit can also be used to demultiplexthe TDM optical input signal S_(in) to extract any channels inadditional stages of this optical gate circuit with thewavelength-division demultiplexer 30.

Embodiment 17

FIG. 48 shows a circuit configuration of Embodiment 17, in which theparametric circuit of FIG. 35 is connected in a multi-stageconfiguration to perform time-division multiplexing of input pulsesignals S_(in1), S_(in2).

In this case, an optical clock signal C which is a pulsed signal wave ofcarrier frequency ω_(S) (refer to FIG. 49A) is input through an opticalcirculator 38₁ into port 20b of the optical directional coupler 20₁ inthe first-stage optical gate circuit. The first optical input signalS_(in1) which is a pulsed pump wave of carrier frequency ω_(P) (refer toFIG. 49B) is input into port 20a. At this time, an optical output signalS_(out1) (FWM wave) of carrier frequency ω_(f) (=2ω_(P) -ω_(S)) isgenerated in the timeslots (t₂, t₄) of the first input signal S_(in1) inthe nonlinear optical medium 12₁ and is output together with the opticalclock signal C' amplified in the active timeslots (t₂, t₄) (refer toFIG. 49C) from the optical circulator 38₁.

The optical clock signal C' and the optical output signal S_(out1) areinput into port 20b of the optical directional coupler 20₂ through theoptical circulator 38₂ of the second-stage optical gate circuit. In themeantime, the second optical input signal S_(in2) which is a pulsed pumpwave of carrier frequency ω_(P) (refer to FIG. 49D) is input into port20a. At this time, an optical output signal (FWM wave) S_(out2) ofcarrier frequency ω_(f) (=2ω_(P) -ω_(S)) is generated in the activetimeslots (t₁, t₃) of the second optical input signal S_(in2) in thenonlinear optical medium 12₂ and is output from port 20b together withthe optical clock signal C" amplified in the timeslots (t₁, t₃) (referto FIG. 49E).

Similarly, additional optical input signals can be multiplexed byfurther connecting additional optical gate circuits.

The wavelength filter 13 blocks the optical clock signal C", and passesonly the TDM optical output signal S_(out2) of carrier frequency ω_(f)(refer to FIG. 49F). Accordingly, the optical circuit of this embodimentgenerates TDM optical output signal S_(out2) of carrier frequency ω_(f)from the two optical input signals S_(in2) of carrier frequency ω_(S).

Embodiment 18

FIGS. 50, 51 show an application of the optical parametric circuit to anoptical waveform sampling circuit for observing optical signals.

The feature of the operating mode of the parametric circuit of thisembodiment is that a pulsed signal wave of carrier frequency ω_(S) isinjected together with a pulsed pump wave of carrier frequency up havinga comparatively narrower pulse width (than that of the target pulsewave) to generate an FWM wave of carrier frequency ω_(f) (=2ω_(P)-ω_(S)). The parametric circuit is provided with a photodetector 40 todetect the FWM wave of carrier frequency ω_(f) and a display 41 as adisplay means for displaying the detected signal waveform from thephotodetector.

In this embodiment, a pulsed pump wave P having a repetition frequencyf+Δf is used to sample a pulsed signal wave S having a repetitionfrequency (bit rate) f, where the pulse width of the pump wave P isnarrower than that of the pulsed signal wave S. The pulsed signal wave Sof carrier frequency ω_(S) (refer to FIG. 52A) and a pulsed pump wave Pof carrier frequency ω_(P) (refer to FIG. 52B) produce an FWM wave F ofcarrier frequency ω_(f) (=2ω_(P) -ω_(S)) (refer to FIG. 52C) having awaveform in which the pulsed pump wave P is amplitude-modulated by thepulsed signal wave S. The envelop of the FWM wave F (shown by dashedcurve in FIG. 52C) having a repetition frequency Δf is obtained bydetecting wave F with a photodetector 40 having a suitable bandwidth(refer to FIG. 52D).

FIG. 50 shows an optical waveform sampling circuit which uses theoptical parametric circuit shown in FIG. 22. Also, FIG. 51 shows anoptical waveform sampling circuit which uses the optical parametriccircuit shown in FIG. 40A. In FIGS. 50 and 51, the optical waveformsampling circuits are provided with a display 41 to display the waveformof the defected signal output from the photodetector 40.

What is claimed is:
 1. An optical parametric circuit comprising:anonlinear optical medium for generating optical waves having carrierangular frequencies ω_(f1), ω_(f2), . . . ω_(fN) from optical waveshaving carrier angular frequencies ω_(S1), ω_(S2), . . . ω_(SN), ω_(P1),and ω_(P2), where ω_(fj) =ω_(P1) +ω_(P2) -ω_(Sj) (j=1,2, . . . N); anoptical directional coupler having a first input port, second inputport, first output port and second output port, for dividing opticalwaves having carrier angular frequencies ω_(Sj), ω_(P1), ω_(P2) andω_(fj) into two optical waves of equal intensities and polarizationstates, respectively; a first dispersive optical medium having a lengthdimension L₁ and a propagation constant K₁ (ω), for connecting the firstoutput port of said optical directional coupler with one end of saidnonlinear optical medium; a second dispersive optical medium having alength dimension L₂ and a propagation constant K₂ (ω), for connectingthe second output port of said optical directional coupler with otherend of said nonlinear optical medium; wherein signal waves havingcarrier angular frequencies ω_(S1), ω_(S2), . . . ω_(SN) and pump waveshaving carrier angular frequencies ω_(P1), ω_(P2) are injected into thefirst input port of said optical directional coupler so as to outputfour-wave-mixing waves having carrier angular frequencies ω_(f1),ω_(f2), . . . ω_(fN) generated in said nonlinear optical medium from thesecond input port of said optical directional coupler, and wherein saidcarrier angular frequencies ω_(Sj), ω_(P1), ω_(P2), and ω_(fj) arerelated by an expression:

    {K.sub.2 (ω.sub.fj)+K.sub.2 (ω.sub.Sj)-K.sub.2 (ω.sub.P1)-K.sub.2 (ω.sub.P2)}L.sub.2 ={K.sub.1 (ω.sub.fj)+K.sub.1 (ω.sub.Sj)-K.sub.1 (ω.sub.P1)-K.sub.1 (ω.sub.P2)}L.sub.1 +(2n-1±α)π

where n is an integer and an allowable error α is in a range 0≦α<1/2. 2.An optical parametric circuit comprising:a nonlinear optical medium forgenerating optical waves having carrier angular frequencies ω_(f1),ω_(f2), . . . ω_(fN) from optical waves having carrier angularfrequencies ω_(S1), ω_(S2), . . . ω_(SN), ω_(P1), and ω_(P2), whereω_(fj) =ω_(P1) +ω_(P2) -ω_(Sj) (j=1,2, . . . N); an optical directionalcoupler having a first input port, second input port, first output portand second output port, for dividing optical waves having carrierangular frequencies ω_(Sj), ω_(P1), ω_(P2) and ω_(fj) into two opticalwaves of equal intensities and polarization states, respectively; afirst dispersive optical medium having a length dimension L₁ and apropagation constant K₁ (ω), for connecting the first output port ofsaid optical directional coupler with one end of said nonlinear opticalmedium; a second dispersive optical medium having a length dimension L₂and a propagation constant K₂ (ω), for connecting the second output portof said optical directional coupler with other end of said nonlinearoptical medium; wherein pump waves having carrier angular frequenciesω_(P1), ω_(P2) are injected into the first input port of said opticaldirectional coupler and signal waves having carrier angular frequenciesω_(S1), ω_(S2), . . . ω_(SN) are injected into the second input port ofsaid optical directional coupler so as to output said signal waveshaving carrier angular frequencies ω_(S1), ω_(S2), . . . ω_(SN)amplified in said nonlinear optical medium together withfour-wave-mixing waves having carrier angular frequencies ω_(f1),ω_(f2), . . . ω_(fN) generated in said nonlinear optical medium from thesecond input port of said optical directional coupler, and wherein saidcarrier angular frequencies ω_(Sj), ω_(P1), ω_(P2), and ω_(fj) arerelated by an expression:

    {K.sub.2 (ω.sub.fj)+K.sub.2 (ω.sub.Sj)-K.sub.2 (ω.sub.P1)-K.sub.2 (ω.sub.P2)}L.sub.2 ={K.sub.1 (ω.sub.fj)+K.sub.1 (ω.sub.Sj)-K.sub.1 (ω.sub.P1)-K.sub.1 (ω.sub.P2)}L.sub.1 +(2n±α)π

where n is an integer and an allowable error α is in a range 0≦α<1/2. 3.An optical parametric circuit comprising:a nonlinear optical medium forgenerating optical waves having carrier angular frequencies ω_(f1),ω_(f2), . . . ω_(fN) from optical waves having carrier angularfrequencies ω_(S1), ω_(S2), . . . ω_(SN), ω_(P1), and ω_(P2), whereω_(fj) =ω_(P1) +ω_(P2) -ω_(Sj) (j=1,2, . . . N); an optical directionalcoupler having a first input port, second input port, first output portand second output port, for dividing optical waves having carrierangular frequencies ω_(Sj), ω_(P1), ω_(P2) and ω_(fj) into two opticalwaves of equal intensities and polarization states, respectively; afirst dispersive optical medium having a length dimension L₁ and apropagation constant K₁ (ω), for connecting the first output port ofsaid optical directional coupler with one end of said nonlinear opticalmedium; a second dispersive optical medium having a length dimension L₂and a propagation constant K₂ (ω), for connecting the second output portof said optical directional coupler with other end of said nonlinearoptical medium; wherein pump waves having carrier angular frequenciesω_(P1), ω_(P2) are injected into the first input port of said opticaldirectional coupler and signal waves having carrier angular frequenciesω_(S1), ω_(S2), . . . ω_(SN) are injected into the second input port ofsaid optical directional coupler so as to output pump waves havingcarrier angular frequencies ω_(P1), ω_(P2) together withfour-wave-mixing waves having carrier angular frequencies ω_(f1),ω_(f2), . . . ω_(fN) generated in said nonlinear optical medium from thefirst input port of said optical directional coupler and to output saidsignal waves having carrier angular frequencies ω_(S1), ω_(S2), . . .ω_(SN) amplified in said nonlinear optical medium from the second inputport of said optical directional coupler, and wherein said carrierangular frequencies ω_(Sj), ω_(P1), ω_(P2), and ω_(fj) are related by anexpression:

    {K.sub.2 (ω.sub.fj)+K.sub.2 (ω.sub.Sj)-K.sub.2 (ω.sub.P1)-K.sub.2 (ω.sub.P2)}L.sub.2 ={K.sub.1 (ω.sub.fj)+K.sub.1 (ω.sub.Sj)-K.sub.1 (ω.sub.P1)-K.sub.1 (ω.sub.P2)}L.sub.1 +(2n-1±α)π

where n is an integer and an allowable error α is in a range 0≦α<1/2. 4.An optical parametric circuit as claimed in one of claims 1 to 3,wherein the carrier angular frequencies ω_(Sj) (j=1, 2, . . . N) of saidsignal waves and the carrier angular frequencies ω_(P1) and ω_(P2) ofsaid pump waves are related by an expression:

    ω.sub.P1 <ω.sub.Sj <ω.sub.P2.


5. An optical parametric circuit as claimed in one of claims 1 to 3,wherein said optical directional coupler, said nonlinear optical mediumand said first and second dispersive optical media arepolarization-maintaining type.
 6. An optical parametric circuit asclaimed in one of claims 1 to 3, wherein said circuit is provided with acompensating means for compensating polarization dispersions in saidoptical directional coupler, said nonlinear optical medium and saidfirst and second dispersive optical media.
 7. An optical parametriccircuit as claimed in claim 5, wherein two components of each electricalfield of said signal waves, said pump waves and said four-wave-mixingwaves polarized along two optic axes of said circuit are interchangedfrom one optic axis to another optic axis at points in said circuitwhich compensate total polarization dispersion in said circuit.
 8. Anoptical parametric circuit as claimed in one of claims 1 and 2, whereinsaid pump waves are injected so as to equalize conversion gains(expressed as four-wave-mixing wave intensity/signal wave intensity) intwo optic axes of said nonlinear optical medium.
 9. An opticalparametric circuit as claimed in one of claims 2 and 3, wherein saidpump waves are injected so as to equalize signal wave amplificationgains in two optic axes of said nonlinear optical medium.
 10. An opticalparametric circuit as claimed in one of claims 1 to 3, wherein saidsignal waves or said pump waves are angular-modulated.
 11. An opticalparametric circuit as claimed in claim 10, wherein amounts of angularmodulation φ_(Sj) (t)(j=1,2, . . . N) of said signal waves at time t andamounts of angular modulations φ_(P1) (t) and φ_(P2) (t) of said pumpwaves at time t are related by an expression:

    φ.sub.P1 (t)+φ.sub.P2 (t)-φ.sub.Sj (t)=0.


12. An optical parametric circuit as claimed in one of claims to 3,wherein optical intensities of said pump waves are modulatedsynchronously with optical intensities of said signal waves.
 13. Anoptical parametric circuit as claimed in claim 1, wherein said circuitis provided with a multiplexing means for multiplexing said signal wavesand said pump waves; andoutput waves from said multiplexing means areinput into the first input port of said optical directional coupler. 14.An optical parametric circuit as claimed in claim 1, wherein saidcircuit is provided with a blocking means for blocking said signal wavesor said pump waves output from the first input port of said opticaldirectional coupler.
 15. An optical parametric circuit as claimed in oneof claims 2 and 3, wherein said circuit is provided with a blockingmeans for blocking said pump waves or said four-wave-mixing waves outputfrom the first input port of said optical directional coupler.
 16. Anoptical parametric circuit as claimed in one of claims 1 and 2, whereinsaid circuit is provided with a filtering means for passing only saidfour-wave-mixing waves output from the second input port of said opticaldirectional coupler.
 17. An optical parametric circuit as claimed in oneof claims 2 and 3, wherein said circuit is provided with a filteringmeans for passing only said signal waves output from the second inputport of said optical directional coupler.
 18. An optical parametriccircuit as claimed in claim 2, wherein said circuit is provided with ameans for separating said signal waves input into the second input portof said optical directional coupler, from said signal waves and saidfour-wave-mixing waves output from the second input port of said opticaldirectional coupler.
 19. An optical parametric circuit as claimed inclaim 2, wherein said circuit is provided with a means for separatingsaid signal waves and said four-wave-mixing waves, both said signalwaves and said four-wave-mixing waves being output from the second inputport of said optical directional coupler.
 20. An optical parametriccircuit as claimed in claim 3, wherein said circuit is provided with ameans for separating said signal waves input into the second input portof said optical directional coupler from said signal waves output fromthe second input port of said optical directional coupler.
 21. Anoptical circuit comprising:a wavelength-division multiplexer formultiplexing an optical input signal having a carrier angular frequencyω_(S) and optical gate signals having carrier angular frequenciesω_(P1k), ω_(P2k) synchronized to said optical input signal and excitedin a kth timeslot (k is an integer) of said optical input signal; anoptical parametric circuit claimed in claim 1 for inputting opticalwaves output from said wavelength-division multiplexer to the firstinput port of said optical directional coupler and outputting opticalwaves having a carrier angular frequency ω_(fk) (=ω_(P1k) +ω_(P2k)-ω_(S)) in said kth timeslot from said second input port of said opticaldirectional coupler; and a wavelength-division demultiplexer forseparating said optical waves having carrier angular frequency ω_(fk)output from said optical parametric circuit for each k.
 22. An opticalcircuit comprising a multi-stage serial circuit arrangement of theoptical parametric circuit claimed in claim 13, wherein:a 1-stageoptical parametric circuit receives an optical input signal having acarrier angular frequency ω_(S) 0 and first optical gate signals havingcarrier angular frequencies ω_(P1) 1, ω_(P2) 1 synchronized to saidoptical input signal, and outputs an optical output signal havingcarrier angular frequency ω_(S1) (=ω_(P1) 1 +ω_(P2) 1 -ω_(S) 0); and ann-stage optical parametric circuit (n is an integer of two or more)receives an optical output signal having a carrier angular frequencyω_(S) n-1 output from a (n-1)-stage optical parametric circuit and nthoptical gate signals having carrier angular frequencies ω_(P1) n, ω_(P2)n synchronized to said optical output signal having carrier angularfrequency ω_(S) n-1, and outputs an optical output signal having carrierangular frequency ω_(Sn) (=ω_(P1) n +ω_(P2) n -ω_(S) n-1).
 23. Anoptical circuit comprising a multi-stage serial circuit arrangement ofoptical parametric circuit claimed in claim 19, wherein:a 1-stageoptical parametric circuit receives an optical input signal having acarrier angular frequency ω_(S) 0 and first optical gate signals havingcarrier angular frequencies ω_(P1) 1, ω_(P2) 1 synchronized to saidoptical input signal, and outputs an optical output signal havingcarrier angular frequency ω_(S) 1 (=ω_(P1) 1 +ω_(P2) 1 -ω_(S) 0); and ann-stage optical parametric circuit (n is an integer of two or more)receives an optical output signal having a carrier angular frequencyω_(S) n-1 output from a (n-1)-stage optical parametric circuit and nthoptical gate signals having carrier angular frequencies ω_(P1) n, ω_(P2)n synchronized to said optical output signal having carrier angularfrequency ω_(S) n-1, and outputs an optical output signal having carrierangular frequency ω_(Sn) (=ω_(P1) n +ω_(P2) n,-ω_(S) 0).
 24. An opticalcircuit comprising a multi-stage serial circuit arrangement of opticalparametric circuit claimed in claim 19, wherein:a 1-stage opticalparametric circuit receives an optical input signal having a carrierangular frequency ω_(S) 0 and first optical gate signals having carrierangular frequencies ω_(P1) 1, ω_(P2) 1 synchronized to said opticalinput signal, and outputs an optical output signal having carrierangular frequency ω_(S) 0 and an optical output signal having carrierangular frequency ω_(S) 1 (=ω_(P1) 1 +ω_(P2) 1 -ω_(S) 0); and an n-stageoptical parametric circuit (n is an integer of two or more) receives anoptical output signal having a carrier angular frequency ω_(S) 0 outputfrom a (n-1)-stage optical parametric circuit and nth optical gatesignals having carrier angular frequencies ω_(P1) n, ω_(P2) nsynchronized to said optical output signal having carrier angularfrequency ω_(S) 0, and outputs an optical output signal having carrierangular frequency ω_(S) 0 and an optical output signal having carrierangular frequency ω_(S) n (=ω_(P1) n +ω_(P2) n -ω_(S) 0).
 25. An opticalcircuit comprising a multi-stage serial circuit arrangement of opticalparametric circuit claimed in claim 18, wherein:a 1-stage opticalparametric circuit receives an optical input signal having a carrierangular frequency ω_(S) and first optical gate signals having carrierangular frequencies ω_(P) +Δω₁, ω_(P) -Δω₁ synchronized to said opticalinput signal, and outputs optical output signals having carrier angularfrequencies ω_(S) and ω_(f) (=2ω_(P) -ω_(S)); and an n-stage opticalparametric circuit (n is an integer of two or more) receives saidoptical output signals having carrier angular frequencies ω_(S) andω_(f) output from a (n-1)-stage optical parametric circuit and nthoptical gate signals having carrier angular frequencies ω_(P) +Δω_(n),ω_(P) -Δω_(n) synchronized to said optical output signals output fromsaid (n-1)-stage optical parametric circuit, and outputs optical outputsignals having carrier angular frequencies ω_(S) and ω_(f), and saidoptical circuit further comprising a means for filtering only an opticalwave having a carrier angular frequency ω_(f) from optical outputsignals of a final-stage optical parametric circuit.
 26. An opticalcircuit comprising:an optical parametric circuit claimed in one ofclaims 1 and 2 for receiving measured optical pulses having a carrierangular frequency ω_(S) and sampling optical pulses having a carrierangular frequency ω_(P) whose pulse width is not more than a pulse widthof said measured optical pulses, and outputting an optical wave of acarrier angular frequency ω_(f) (=2ω_(P) -ω_(S)); a photodetector fordetecting said optical wave having a carrier angular frequency ω_(f) ;and a display means for displaying an output signal from saidphotodetector.